Abstract
By using a method based upon the principle of the Briot-Bouquet differential subordination, we obtain a sharp result for p-valently starlikeness of certain normalized and multivalently analytic functions. Our investigation of such families of multivalently analytic functions is motivated essentially by a recent study by Nunokawa et al. [M. Nunokawa, S. Owa, T. Sekine, R. Yamakawa, H. Saitoh and J. Nishiwaki, On certain multivalent functions, Internat. J. Math. Math. Sci. 2007 (2007) 1-5. Article ID 72393]. We also give an answer to the open problem which was posed in the aforementioned article by Nunokawa et al. (C) 2010 Elsevier Ltd. All rights reserved.